DOCSLIB.ORG

The Creation-Discovery-View : Towards a Possible Explanation of Quantum Reality

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Creation-Discovery-View : Towards a Possible Explanation of Quantum Reality The creation-discovery-view : towards a possible explanation of quantum reality¤ Diederik Aerts and Bob Coecke CLEA, Free University of Brussels, Pleinlaan 2, 1050 Brussels, Belgium. e-mails: [email protected], [email protected] Abstract We present a realistic interpretation for quantum mechanics that we have called the 'creation discovery view' and that is being developed in our group in Brussels. In this view the change of state of a quantum entity during an experiment is taken to be a 'real change' under inuence of the experiment, and the quantum probability that corresponds to the experi- ment is explained as due to a lack of knowledge of a deeper deterministic reality of the measurement process. The technical mathematical theory underlying the creation discovery view that we are elaborating we have called the 'hidden measurement formalism'. We present a simple physical example: the 'quantum machine', where we can illustrate easily how the quantum structure arises as a consequence of the two mentioned e®ects, a real change of the state, and a lack of knowledge about a deeper reality of the measurement process. We analyze non-locality in the light of the creation discovery view, and show that we can understand it if we accept that also the basic concept of 'space' is partly due to a creation: when a detection of a quantum entity in a non-local state occurs, the physical act of detection itself 'creates' partly the 'place' of the quantum entity. In this way the creation discovery view introduces a new ontology for space: space is not the all embracing theater, where all 'real' objects have their place, but it is the structure that governs a special type of relations (the space-like relations) between macroscopic physical entities. We bring for- ward a number of elements that show the plausibility of the approach and also analyze the way in which the presence of Bell-type correlated events can be incorporated. ¤Published as: Aerts, D. and Coecke, B., 1999, \The creation-discovery-view : towards a possible explanation of quantum reality", in Language, Quantum, Music, eds. Dalla Chiara, M.L., Kluwer Academic, Dordrecht. 1 1 Introduction The creation discovery view and together with it its technically underlying hid- den measurement formalism has been elaborated from the early eighties on, and many aspects of it have been exposed in di®erent places [6, 7, 12, 13, 15, 16, 19, 20, 22, 23, 30, 31, 32, 33, 34, 35, 36]. In this paper we give an overview of the most important of these aspects. Quantum mechanics was originally introduced as a non-commutative ma- trix calculus of observables by Werner Heisenberg [41] and parallel as a wave mechanics by Erwin SchrÄodinger [43]. These two structurally very di®erent theories could explain fruitfully the early observed quantum phenomena. Al- ready in the same year the two theories were shown to be realizations of the same, more abstract, ket-bra formalism by Dirac [38]. Only some years later, in 1934, John Von Neumann put forward a rigorous mathematical framework for quantum theory in an in¯nite dimensional separable complex Hilbert space [46]. Matrix mechanics and wave mechanics appear as concrete realizations: the ¯rst one if the Hilbert space is l2, the collection of all square summable complex numbers, and the second one if the Hilbert space is L2, the collection of all square integrable complex functions. The formulation of quantum mechanics in the abstract framework of a complex Hilbert space is now usually referred to as the 'standard quantum mechanics'. The basic concepts - the vectors of the Hilbert space representing the states of the system and the self-adjoint operators representing the observables - in this standard quantum mechanics are abstract mathematical concepts de¯ned mathematically in and abstract mathematical space. Several approaches have generalized the standard theory starting from more physically de¯ned basic concepts. John Von Neumann and Garett Birkho® have initiated one of these approaches [29] were they analyze the di®erence between quantum and classical theories by studying the 'experimental propositions'. They could show that for a given physical system classical theories have a Boolean lattice of experimental propositions while for quantum theory the lattice of experimental propositions is not Boolean. Similar fundamental structural di®erences between the two theories have been investigated by concentrating on di®erent basic concepts. The collection of observables of a classical theory was shown to be a commutative algebra while this is not the case for the collection of quantum observables [40, 44]. Luigi Accardi and Itamar Pitowski obtained an analogous result by concentrating on the probability models connected to the two theories: classical theories have a Kolmogorovian probability model while the probability model of a quantum theory is non Kolmogorovian [1, 42]. The fundamental structural di®erences between the two types of theories, quantum and classical, in di®erent categories, was interpreted as indicating also a fundamental di®erence on the level of the nature of the reality that both theories describe: the micro world should be 'very di®erent' from the macro world. This state of a®airs was very convincing also because concrete attempts 2 to understand quantum mechanics in a classical way had failed as well: e.g. the many 'physical' hidden variable theories that had been tried out [45]. The structural di®erence between quantum theories and classical theories (Boolean lattice versus non- Boolean lattice of propositions, commutative algebra ver- sus non commutative algebra of observables and Kolmogorovian versus non Kolmogorovian probability structure) had been investigated mostly mathemat- ically and not much understanding of the physical meaning of the structural di®erences had been gained during all these years. The ¯rst step that led to the creation discovery view and its underlying hidden measurement formalism was a breakthrough in the understanding of the physical origin of these mathematical structural di®erences between quantum and classical theories. Indeed, one of the authors found in the early eighties a way to identify the physical aspects that are at the origin of the structural di®erences [3, 6, 7]. Let us summarize these ¯ndings: it are mainly two aspects that determine the mathematical structural di®erences between classical and quantum theories in the di®erent categories: We have a quantum-like theory describing a system under investigation if the measurements needed to test the properties of the system are such that: (1) The measurements are not just observations but provoke a real change of the state of the system. (2) There exists a lack of knowledge about the reality of what happens during the measurement process. The presence of these two aspects is su±cient to render the description of the system under consideration quantum-like. It is the lack of knowledge (2) that is theoretically structured in a non Kolmogorovian probability model. In a certain sense it is possible to interpret the second aspect, the presence of the lack of knowledge on the reality of the measurement process, as the presence of 'hidden measurements' instead of 'hidden variables'. Indeed, if a measurement is performed with the presence of such a lack of knowledge, then this is actually the classical mixture of a set of classical hidden measurements, were for such a classical hidden measurement there would be no lack of knowledge. In an analogous way as in a hidden variable theory, the quantum state is a classical mixture of classical states. This is the reason why we have called the underlying theory of the creation discovery view the hidden measurement formalism. It is possible to illustrate the creation discovery view and the hidden measurement aspect in a very simple way by using a mechanical model that was introduced in [5, 16, 7] and that we have called the quantum machine. This is the subject of next section. 3 2 The Quantum Machine. Several aspects of the quantum machine have been presented in di®erent occa- sions [6, 7, 8, 9, 10, 15, 19, 20] and we shall therefore introduce here only the basic aspects. The machine that we consider consists of a physical entity S that is a point particle P that can move on the surface of a sphere, denoted surf, with center O and radius 1. The unit-vector v where the particle is located on surf represents the state pv of the particle (see Fig 1,a). For each point u surf, we introduce the following measurement eu. We consider the diamet- rically2 opposite point u, and install a piece of elastic of length 2, such that it is ¯xed with one of its¡end-points in u and the other end-point in u. Once the elastic is installed, the particle P falls from its original place v orthogonally¡ onto the elastic, and sticks on it (Fig 1,b). Then the elastic breaks and the particle P , attached to one of the two pieces of the elastic (Fig 1,c), moves to one of the two end-points u or u (Fig 1,d). Depending on whether the particle P arrives ¡ u u in u (as in Fig 1) or in u, we give the outcome o1 or o2 to eu. We can easily calculate the probabilities¡ corresponding to the two possible outcomes. v v P u u Fig 1 : A representation of the quantum machine. q q In (a) the physical entity P is in state pv in the P point v, and the elastic corresponding to the mea- surement eu is installed between the two diametri- -u -u cally opposed points u and u. In (b) the particle (a) ¡ (b) P falls orthogonally onto the elastic and stick to u u it.
Load more

Recommended publications
  • The Emergence of a Classical World in Bohmian Mechanics
    The Emergence of a Classical World in Bohmian Mechanics Davide Romano Lausanne, 02 May 2014 Structure of QM • Physical state of a quantum system: - (normalized) vector in Hilbert space: state-vector - Wavefunction: the state-vector expressed in the coordinate representation Structure of QM • Physical state of a quantum system: - (normalized) vector in Hilbert space: state-vector; - Wavefunction: the state-vector expressed in the coordinate representation; • Physical properties of the system (Observables): - Observable ↔ hermitian operator acting on the state-vector or the wavefunction; - Given a certain operator A, the quantum system has a definite physical property respect to A iff it is an eigenstate of A; - The only possible measurement’s results of the physical property corresponding to the operator A are the eigenvalues of A; - Why hermitian operators? They have a real spectrum of eigenvalues → the result of a measurement can be interpreted as a physical value. Structure of QM • In the general case, the state-vector of a system is expressed as a linear combination of the eigenstates of a generic operator that acts upon it: 퐴 Ψ = 푎 Ψ1 + 푏|Ψ2 • When we perform a measure of A on the system |Ψ , the latter randomly collapses or 2 2 in the state |Ψ1 with probability |푎| or in the state |Ψ2 with probability |푏| . Structure of QM • In the general case, the state-vector of a system is expressed as a linear combination of the eigenstates of a generic operator that acts upon it: 퐴 Ψ = 푎 Ψ1 + 푏|Ψ2 • When we perform a measure of A on the system |Ψ , the latter randomly collapses or 2 2 in the state |Ψ1 with probability |푎| or in the state |Ψ2 with probability |푏| .
    [Show full text]
  • Aspects of Loop Quantum Gravity
    Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models .
    [Show full text]
  • Quantum Mechanics As a Limiting Case of Classical Mechanics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE Quantum Mechanics As A Limiting Case provided by CERN Document Server of Classical Mechanics Partha Ghose S. N. Bose National Centre for Basic Sciences Block JD, Sector III, Salt Lake, Calcutta 700 091, India In spite of its popularity, it has not been possible to vindicate the conven- tional wisdom that classical mechanics is a limiting case of quantum mechan- ics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment. PACS no. 03.65.Bz 1 I. INTRODUCTION One of the most puzzling aspects of quantum mechanics is the quantum measurement problem which lies at the heart of all its interpretations. With- out a measuring device that functions classically, there are no ‘events’ in quantum mechanics which postulates that the wave function contains com- plete information of the system concerned and evolves linearly and unitarily in accordance with the Schr¨odinger equation. The system cannot be said to ‘possess’ physical properties like position and momentum irrespective of the context in which such properties are measured. The language of quantum mechanics is not that of realism. According to Bohr the classicality of a measuring device is fundamental and cannot be derived from quantum theory. In other words, the process of measurement cannot be analyzed within quantum theory itself. A simi- lar conclusion also follows from von Neumann’s approach [1].
    [Show full text]
  • The Quantum Epoché
    Accepted Manuscript The quantum epoché Paavo Pylkkänen PII: S0079-6107(15)00127-3 DOI: 10.1016/j.pbiomolbio.2015.08.014 Reference: JPBM 1064 To appear in: Progress in Biophysics and Molecular Biology Please cite this article as: Pylkkänen, P., The quantum epoché, Progress in Biophysics and Molecular Biology (2015), doi: 10.1016/j.pbiomolbio.2015.08.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT The quantum epoché Paavo Pylkkänen Department of Philosophy, History, Culture and Art Studies & the Academy of Finland Center of Excellence in the Philosophy of the Social Sciences (TINT), P.O. Box 24, FI-00014 University of Helsinki, Finland. and Department of Cognitive Neuroscience and Philosophy, School of Biosciences, University of Skövde, P.O. Box 408, SE-541 28 Skövde, Sweden [email protected] Abstract. The theme of phenomenology and quantum physics is here tackled by examining some basic interpretational issues in quantum physics. One key issue in quantum theory from the very beginning has been whether it is possible to provide a quantum ontology of particles in motion in the same way as in classical physics, or whether we are restricted to stay within a more limited view of quantum systems, in terms of complementary but mutually exclusiveMANUSCRIPT phenomena.
    [Show full text]
  • Coherent States and the Classical Limit in Quantum Mechanics
    Coherent States And The Classical Limit In Quantum Mechanics 0 ħ ¡! Bram Merten Radboud University Nijmegen Bachelor’s Thesis Mathematics/Physics 2018 Department Of Mathematical Physics Under Supervision of: Michael Mueger Abstract A thorough analysis is given of the academical paper titled "The Classical Limit for Quantum Mechanical Correlation Functions", written by the German physicist Klaus Hepp. This paper was published in 1974 in the journal of Communications in Mathematical Physics [1]. The part of the paper that is analyzed summarizes to the following: "Suppose expectation values of products of Weyl operators are translated in time by a quantum mechanical Hamiltonian and are in coherent states 1/2 1/2 centered in phase space around the coordinates ( ¡ ¼, ¡ »), where (¼,») is ħ ħ an element of classical phase space, then, after one takes the classical limit 0, the expectation values of products of Weyl operators become ħ ¡! exponentials of coordinate functions of the classical orbit in phase space." As will become clear in this thesis, authors tend to omit many non-trivial intermediate steps which I will precisely include. This could be of help to any undergraduate student who is willing to familiarize oneself with the reading of academical papers, but could also target any older student or professor who is doing research and interested in Klaus Hepp’s work. Preliminary chapters which will explain all the prerequisites to this paper are given as well. Table of Contents 0 Preface 1 1 Introduction 2 1.1 About Quantum Mechanics . .2 1.2 About The Wave function . .2 1.3 About The Correspondence of Classical and Quantum mechanics .
    [Show full text]
  • Quantum Theory and the Structure of Space-Time
    Quantum theory and the structure of space-time Tejinder Singh Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India ABSTRACT We argue that space and space-time emerge as a consequence of dynamical collapse of the wave function of macroscopic objects. Locality and separability are properties of our approximate, emergent universe. At the fundamental level, space-time is non-commutative, and dynamics is non-local and non-separable. I. SPACE-TIME IS NOT THE PERFECT ARENA FOR QUANTUM THEORY Space-time is absolute, in conventional classical physics. Its geometry is determined dy- namically by the distribution of classical objects in the universe. However, the underlying space-time manifold is an absolute given, providing the arena in which material bodies and fields exist. The same classical space-time arena is carried over to quantum mechanics and to quantum field theory, and it works beautifully there too. Well, almost! But not quite. In this essay we propose the thesis that the troubles of quantum theory arise because of the illegal carry-over of this classical arena. By troubles we mean the quantum measurement problem, the spooky action at a distance and the peculiar nature of quantum non-locality, the so-called problem of time in quantum theory, the extreme dependence of the theory on its classical limit, and the physical meaning of the wave function [1]. We elaborate on these in the next section. Then, in Section III, we propose that the correct arena for quantum theory is a non-commutative space-time: here there are no troubles. Classical space-time emerges as an approximation, as a consequence of dynamical collapse of the wave function.
    [Show full text]
  • Path Integrals in Quantum Mechanics
    Path Integrals in Quantum Mechanics Emma Wikberg Project work, 4p Department of Physics Stockholm University 23rd March 2006 Abstract The method of Path Integrals (PI’s) was developed by Richard Feynman in the 1940’s. It offers an alternate way to look at quantum mechanics (QM), which is equivalent to the Schrödinger formulation. As will be seen in this project work, many "elementary" problems are much more difficult to solve using path integrals than ordinary quantum mechanics. The benefits of path integrals tend to appear more clearly while using quantum field theory (QFT) and perturbation theory. However, one big advantage of Feynman’s formulation is a more intuitive way to interpret the basic equations than in ordinary quantum mechanics. Here we give a basic introduction to the path integral formulation, start- ing from the well known quantum mechanics as formulated by Schrödinger. We show that the two formulations are equivalent and discuss the quantum mechanical interpretations of the theory, as well as the classical limit. We also perform some explicit calculations by solving the free particle and the harmonic oscillator problems using path integrals. The energy eigenvalues of the harmonic oscillator is found by exploiting the connection between path integrals, statistical mechanics and imaginary time. Contents 1 Introduction and Outline 2 1.1 Introduction . 2 1.2 Outline . 2 2 Path Integrals from ordinary Quantum Mechanics 4 2.1 The Schrödinger equation and time evolution . 4 2.2 The propagator . 6 3 Equivalence to the Schrödinger Equation 8 3.1 From the Schrödinger equation to PI’s . 8 3.2 From PI’s to the Schrödinger equation .
    [Show full text]
  • 2. Classical Gases
    2. Classical Gases Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, flying around in a box. Although much of the last section was formulated in the language of quantum mechanics, here we will revert back to classical mechanics. Nonetheless, a recurrent theme will be that the quantum world is never far behind: we’ll see several puzzles, both theoretical and experimental, which can only truly be resolved by turning on ~. 2.1 The Classical Partition Function For most of this section we will work in the canonical ensemble. We start by reformu- lating the idea of a partition function in classical mechanics. We’ll consider a simple system – a single particle of mass m moving in three dimensions in a potential V (~q ). The classical Hamiltonian of the system3 is the sum of kinetic and potential energy, p~ 2 H = + V (~q ) 2m We earlier defined the partition function (1.21) to be the sum over all quantum states of the system. Here we want to do something similar. In classical mechanics, the state of a system is determined by a point in phase space.Wemustspecifyboththeposition and momentum of each of the particles — only then do we have enough information to figure out what the system will do for all times in the future. This motivates the definition of the partition function for a single classical particle as the integration over phase space, 1 3 3 βH(p,q) Z = d qd pe− (2.1) 1 h3 Z The only slightly odd thing is the factor of 1/h3 that sits out front.
    [Show full text]
  • Consciousness, the Unconscious and Mathematical Modeling of Thinking
    entropy Article On “Decisions and Revisions Which a Minute Will Reverse”: Consciousness, The Unconscious and Mathematical Modeling of Thinking Arkady Plotnitsky Literature, Theory and Cultural Studies Program, Philosophy and Literature Program, Purdue University, West Lafayette, IN 47907, USA; [email protected] Abstract: This article considers a partly philosophical question: What are the ontological and epistemological reasons for using quantum-like models or theories (models and theories based on the mathematical formalism of quantum theory) vs. classical-like ones (based on the mathematics of classical physics), in considering human thinking and decision making? This question is only partly philosophical because it also concerns the scientific understanding of the phenomena considered by the theories that use mathematical models of either type, just as in physics itself, where this question also arises as a physical question. This is because this question is in effect: What are the physical reasons for using, even if not requiring, these types of theories in considering quantum phenomena, which these theories predict fully in accord with the experiment? This is clearly also a physical, rather than only philosophical, question and so is, accordingly, the question of whether one needs classical-like or quantum-like theories or both (just as in physics we use both classical and quantum theories) in considering human thinking in psychology and related fields, such as decision Citation: Plotnitsky, A. On science. It comes as no surprise that many of these reasons are parallel to those that are responsible “Decisions and Revisions Which a for the use of QM and QFT in the case of quantum phenomena.
    [Show full text]
  • On the Interpretation of the Quantum Wave Function
    On the interpretation of the quantum wave function Master's thesis Physics and Astronomy Radboud University Nijmegen Supervisors: Prof. R.H.P. Kleiss and H.C. Donker Second corrector: Assoc. Prof. F. Filthaut Han van der Pluijm August 26, 2016 Contents Introduction 3 1 The wave function and its relation to the real world: Ontic and epistemic interpretations of the wave function 5 1.1 Classical states . .6 1.2 A classical particle in phase space . .7 1.3 Example of an incomplete ontic state . 10 1.4 Quantum states . 11 1.4.1 Epistemic and ontic states in quantum theory . 12 2 Ontological models and the PBR no-go theorem 14 2.1 Ontological models . 15 2.2 The structure of PBR's no-go theorem . 16 2.3 Assumptions . 17 2.3.1 Mathematical equivalents . 18 2.4 The proof . 19 3 Spekkens Toy Theory 23 3.1 The knowledge balance principle . 24 3.2 Spekkens' Toy Bit . 26 3.3 Multiple bits . 31 3.4 Parallels with quantum theory . 33 3.4.1 Convex combinations . 33 3.4.2 Coherent superpositions . 34 3.4.3 Interference . 35 4 Mach-Zehnder interferometer in Spekkens toy theory 36 4.1 Setup of the Mach-Zehnder interferometer . 36 4.2 Quantum behaviour . 38 4.3 States of the MZI in Spekkens' toy theory . 41 4.4 Future prospects . 44 5 Conclusion and discussion 45 Bibliography 47 1 Preface The reason I choose to study physics was twofold. On the one hand I was looking for a challenge and on the other hand I wanted to under- stand the world truly.
    [Show full text]
  • Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 6 Calculating Things with Quantum Trajectories
    Pilot-wave theory, Bohmian metaphysics, and the foundations of quantum mechanics Lecture 6 Calculating things with quantum trajectories Mike Towler TCM Group, Cavendish Laboratory, University of Cambridge www.tcm.phy.cam.ac.uk/∼mdt26 and www.vallico.net/tti/tti.html [email protected] – Typeset by FoilTEX – 1 Acknowledgements The material in this lecture is to a large extent a summary of publications by Peter Holland, R.E. Wyatt, D.A. Deckert, R. Tumulka, D.J. Tannor, D. Bohm, B.J. Hiley, I.P. Christov and J.D. Watson. Other sources used and many other interesting papers are listed on the course web page: www.tcm.phy.cam.ac.uk/∼mdt26/pilot waves.html MDT – Typeset by FoilTEX – 2 On anticlimaxes.. Up to now we have enjoyed ourselves freewheeling through the highs and lows of fundamental quantum and relativistic physics whilst slagging off Bohr, Heisenberg, Pauli, Wheeler, Oppenheimer, Born, Feynman and other physics heroes (last week we even disagreed with Einstein - an attitude that since the dawn of the 20th century has been the ultimate sign of gibbering insanity). All tremendous fun. This week - we shall learn about finite differencing and least squares fitting..! Cough. “Dr. Towler, please. You’re not allowed to use the sprinkler system to keep the audience awake.” – Typeset by FoilTEX – 3 QM computations with trajectories Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation P. Holland (2004) “The notion that the concept of a continuous material orbit is incompatible with a full wave theory of microphysical systems was central to the genesis of wave mechanics.
    [Show full text]
  • How Classical Particles Emerge from the Quantum World
    Foundations of Physics manuscript No. (will be inserted by the editor) Dennis Dieks and Andrea Lubberdink How Classical Particles Emerge From the Quantum World Received: date / Accepted: date Abstract The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum parti- cles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with what we know about classical parti- cles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely for- mal significance. This conclusion raises the question of whether the discussions about the status of identical quantum particles have not been misguided from the very start. Keywords identical quantum particles ¢ indistinguishability ¢ classical particles ¢ emergence ¢ classical limit of quantum mechanics PACS 03.65+b 1 Introduction In classical physics, particles are the example par excellence of distinguishable individuals. No two classical particles can be in exactly the same physical state: in D. Dieks Institute for the History and Foundations of Science, Utrecht University P.O.Box 80.010, 3508 TA Utrecht, The Netherlands E-mail: [email protected] 2 Newtonian spacetime different particles will at least occupy different spatial po- sitions at any moment, because of their impenetrability.
    [Show full text]